Relativistic velocity addition from the geometry of momentum space

With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe two ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1+1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1+2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

Recent Progress in Gamow Shell Model Calculations of Drip Line Nuclei

The Gamow shell model (GSM) is a powerful method for the description of the exotic properties of drip line nuclei. Internucleon correlations are included via a configuration interaction framework. Continuum coupling is directly included at basis level by using the Berggren basis, in which, bound, resonance, and continuum single-particle states are treated on an equal footing in the complex momentum plane. Two different types of Gamow shell models have been developed: its first embodiment is that of the GSM defined with phenomenological nuclear interactions, whereas the GSM using realistic nuclear interactions, called the realistic Gamow shell model, was introduced later. The present review focuses on the recent applications of the GSM to drip line nuclei.

Pole skipping and chaos in anisotropic plasma: a holographic study

Recently, a direct signature of chaos in many body system has been realized from the energy density retarded Green’s function using the phenomenon of ‘pole skipping’. Moreover, special locations in the complex frequency and momentum plane are found, known as the pole skipping points such that the retarded Green’s function can not be defined uniquely there. In this paper, we compute the correction/shift to the pole skipping points due to a spatial anisotropy in a holographic system by performing near horizon analysis of EOMs involving different bulk field perturbations, namely the scalar, the axion and the metric field. For vector and scalar modes of metric perturbations we construct the gauge invariant variable in order to obtain the master equation. Two separate cases for every bulk field EOMs is considered with the fluctuation propagating parallel and perpendicular to the direction of anisotropy. We compute the dispersion relation for momentum diffusion along the transverse direction in the shear channel and show that it passes through the first three successive pole skipping points. The pole skipping phenomenon in the sound channel is found to occur in the upper half plane such that the parameters Lyapunov exponent λL and the butterfly velocity vB are explicitly obtained thus establishing the connection with many body chaos.

Quasinormal modes in charged fluids at complex momentum

We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordström black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.

Study of Spin–Spin Correlations between Quark and a Spin-1/2 Composite System

We study the correlation between the fermion composite system and quark spins by using the light-cone quark–diquark model. We do the calculations for u-quark and d-quark in the fermion system by considering different polarization configurations of both. The contribution from scalar and axial-vector diquarks is taken into account. The overlap representation of light-front wavefunctions is used for the calculations. The spin–spin correlations for u and d quarks are presented in transverse impact-parameter plane and transverse momentum plane as well.

Holographic chaos, pole-skipping, and regularity

We investigate the “pole-skipping” phenomenon in holographic chaos. According to pole-skipping, the energy-density Green’s function is not unique at a special point in the complex momentum plane. This arises because the bulk field equation has two regular near-horizon solutions at the special point. We study the regularity of the two solutions more carefully using curvature invariants. In the upper-half $\omega$-plane, one solution, which is normally interpreted as the outgoing mode, is in general singular at the future horizon and produces a curvature singularity. However, at the special point, both solutions are indeed regular. Moreover, the incoming mode cannot be uniquely defined at the special point due to these solutions.

Gas accretion and galactic fountain flows in the Auriga cosmological simulations: angular momentum and metal redistribution

ABSTRACT Using a set of 15 high-resolution magnetohydrodynamic cosmological simulations of Milky Way formation, we investigate the origin of the baryonic material found in stars at redshift zero. We find that roughly half of this material originates from subhalo/satellite systems and half is smoothly accreted from the intergalactic medium. About $90 {{\ \rm per\ cent}}$ of all material has been ejected and re-accreted in galactic winds at least once. The vast majority of smoothly accreted gas enters into a galactic fountain that extends to a median galactocentric distance of ∼20 kpc with a median recycling time-scale of ∼500 Myr. We demonstrate that, in most cases, galactic fountains acquire angular momentum via mixing of low angular momentum, wind-recycled gas with high angular momentum gas in the circumgalactic medium (CGM). Prograde mergers boost this activity by helping to align the disc and CGM rotation axes, whereas retrograde mergers cause the fountain to lose angular momentum. Fountain flows that promote angular momentum growth are conducive to smooth evolution on tracks quasi-parallel to the disc sequence of the stellar mass-specific angular momentum plane, whereas retrograde minor mergers, major mergers, and bar-driven secular evolution move galaxies towards the bulge sequence. Finally, we demonstrate that fountain flows act to flatten and narrow the radial metallicity gradient and metallicity dispersion of disc stars, respectively. Thus, the evolution of galactic fountains depends strongly on the cosmological merger history and is crucial for the chemodynamical evolution of Milky-Way-sized disc galaxies.

On the effect of resonances in the quark-photon vertex

A calculation of hadronic timelike form factors in the Poincaré-covariant Bethe-Salpeter formalism necessitates knowing the analytic structure of the non-perturbative quark-photon vertex in the context of the Poincaré-covariant Bethe-Salpeter formalism. We include, in the interaction between quark and antiquark, the possibility of non-valence effects by introducing pions as explicit degrees of freedom. These encode the presence of intermediate resonances in the Bethe-Salpeter interaction kernel. We calculate the vertex for real as well as complex photon momentum. We show how the vertex reflects now the correct physical picture, with the rho resonance appearing as a pole in the complex momentum plane. A multiparticle branch cut for values of the photon momentum from $ -4m_{\pi}^{2}$-4mπ2 to $ -\infty$-∞ develops. This calculation represents an essential step towards the calculation of timelike form factors in the Bethe-Salpeter approach.